Practise the method.
Example 1
An account starts at−$22. At the end of every day it receives $8. At the end of days 7,14,21, …, a $12 fee is then deducted. What is the first whole day on which the balance, after any fee that day, is at least $168?
Show worked answer
Answer: 30
- After d days, add 8d to the starting −22
- subtract $12 for each complete block of 7 days.
- Check successive weekly blocks and their end−of−day balances.
- The first qualifying balance is on day 30.
Example 2
A quiz has 20 questions. Each correct answer earns 4 points, each wrong answer loses 2, and a blank earns 0. A student's number correct is 2 more than twice the number blank. Their final score is 28. How many answers were wrong?
Show worked answer
Answer: 6
- Let b be blank and w wrong.
- Correct =2b+2
- 3b+w=18.
- The signed score is 4(2b+2)−2w=28.
- Solve the two equations: b=4,w=6.
Example 3
An account starts at−$16. At the end of every day it receives $3. At the end of days 7,14,21, …, a $15 fee is then deducted. What is the first whole day on which the balance, after any fee that day, is at least $13?
Show worked answer
Answer: 20
- After d days, add 3d to the starting −16
- subtract $15 for each complete block of 7 days.
- Check successive weekly blocks and their end−of−day balances.
- The first qualifying balance is on day 20.